However, it's not immediate. You need to have 100 confirmations after you mine a block before the network recognizes that you own the coins, so it's going to take about 16 hours 40 minutes to show up.
What Fjordbit said is correct, except it is 120 confirmations, not 100, meaning they mature ("show up") about 20 hours after having mined them.
(I am a solo miner.)
It seems that's a client thing. The network recognizes them in 100.
https://en.bitcoin.it/wiki/Protocol_rulesFor each input, if the referenced output transaction is coinbase (i.e. only 1 input, with hash=0, n=-1), it must have at least COINBASE_MATURITY (100) confirmations; else reject this transaction
Many pools pay out in 100.